Dynamic Characteristics of the Jet Force on the Flapper of the Pilot Stage in a Flapper Nozzle Servo Valve Under the Flow-Solid Interaction

Xinbei Lü， Jinghui Peng and Songjing Li

（Fluid Control and Automation Systems, Harbin Institute of Technology, Harbin 150001, China）

Abstract: Nowadays, more and more attention has been paid to improve the performance of the nozzle flapper servo valve. As a core part of nozzle flapper servo valve, the armature assembly is af?fected by electromagnetic force, jet force and feedback force at the same time. Due to the complex structure of the pilot stage flow field and the high jet pressure, the prediction of the jet force has al?ways been difficult in modeling the transient motion of the servo valve. Whereupon, a numerical simulation method based on the flow?solid interaction(FSI) is applied to observe the variation of the jet force when the flapper is moving. Different parameters are employed to seek a suitable nu?merical simulation model which can balance the accuracy and computational cost. By comparing with the experiment results, the effectiveness of numerical simulation method in predicting the vari?ation of the jet force and cavitation is verified. By this numerical simulation model, the distribu?tion of flow field and the force on the flapper predicted by the moving and fixed flapper are com?pared. The results show that more dynamic details are achieved by the transient simulation. By analyzing the numerical simulation results of different inlet pressures and flapper vibration frequen?cies, the relationship between the movement of the flapper, the flow field distribution, the jet force and the inlet pressure is established, which provides a theoretical basis for the subsequent modeling of the armature assembly.

Key words: flapper nozzle servo valve；numerical simulation；force variation；flow field

In recent years, the servo valve has played an important role in the industrial field such as aviation, shipbuilding and machinery. As a clas?sical type of servo valve, the flapper nozzle servo valve has been widely used in the industrial field for fast response and large output power. But due to its complicated structure and high work?ing frequency, the spring tube of the armature assembly in the pilot stage of servo valve is of?ten broken during the working process, which limits its wider applications. Therefore, investig?ating the dynamic response of the armature as?sembly and improving its working stability have become the important tasks that need to be done urgently. The jet force generated by the nozzle in the pilot stage is one of the feedback forces act?ing on the armature assembly, and it also plays an important role in the process of armature as?sembly dynamic response. Therefore, establish?ing the relationship between the jet force and the moving flapper in the pilot stage of servo valve has become one of the necessary conditions for elucidating the vibration mechanism of the arma?ture assembly.

The numerical simulation has become one of the important methods to study and improve the performance of the servo valve for its tiny struc?ture and high velocity[1?4]. Nie et al. introduced a numerical simulation method to observe a abras?ive water?jet nozzle based on the multi?phase movement. The results showed that the axial ve?locity and dynamic pressure of the continuous phase in the nozzle had notable axial symmetry,and an extreme point was generated at the axis[5].Zhu et al. invented an novel structure in the dir?ect drive rotary control valve. The flow charac?teristics and fluid torques were analyzed based on the computational fluid dynamics method and experiment, and the effectiveness of improved valve model in reducing the fluid torque had been verified[6]. Yang et al. made a numerical in?vestigation of the manipulation of the flapper?nozzle pilot valve with the continuous minijets located around the main jet of each nozzle. The reduction in the cavitation strength was verified by the numerical simulation under the effect of the continuous minijets[7]. Yuan et al. made the experiment and calculation based on Open?FOAM to observe the distinction between incom?pressible and compressible methods in the cases of non?cavitating and cavitating. The comparis?on results exhibited a better agreement with ex?periment regarding both flow performance and flow structure[8]. Lu et al. used the Large Eddy Simulation turbulent model to analyze the oscil?lation of the flow field in the pilot stage of the double nozzle flapper servo valve. The simula?tion results showed that the pressure on the flap?per is nearly proportional to the flow velocity and inversely proportional to the actual distance between the flapper and the nozzle[9]. Yan et al.investigated the internal characteristics of the de?flector jet valve by a three?dimensional numeric?al model. With the assumption about the flow distribution, the pressure of pilot stage were sig?nificantly enhanced in the numerical simulation,which was also confirmed by the experiments[10?11].Lu et al. discussed the notch flow characteristics to form the large vapor cavity and its surge in?stability characteristics by experimental and nu?merical analysis. The relationship between the notch flow resistance and the surge behavior was analyzed[12]. It can be seen that the CFD method can accurately predict the working characterist?ics of the servo valve flow field. However, the nu?merical simulation of the moving flapper has not yet appeared, which makes the simulation res?ults have certain limitations in predicting the dy?namic characteristics of the armature assembly.

To predict and improve the working per?formance, many methods are applied to establish the relationship between the parameters and per?formance of the servo and related systems. Z Rao and G M Bone derived a new model for the pneumatic servo actuators which were developed using a combination of mechanistic and empiric?al methods. The use of the new model was shown to produce a more accurate solution than previ?ous numerical simulation results comparing with the experiment[13]. Pan et al. analyzed the dis?charge characteristics of servo?valve spool valve under the conditions of laminar and turbulent flow, by which a mathematical model for the ori?fice flow was established. The experiments of the actual spool valve was carried out and the math?ematical model is verified[14]. Saha et al. simu?lated the flow field of the servo valve pilot stage,and observed the characteristics of cavitation. Fi?nally, a relationship between the boundary condi?tions and the distribution of flow field in the pi?lot stage was established for incompressible fluid flow[15?16]. Liu et al. investigated the influences of structure deformation and working media on the dynamic characteristics of electrohydraulic servo valve, by which the mathematical model of elec?trohydraulic servo valve was established. The validity of the model were verified by ANSYS Workbench[17]. Yu and Yin developed a dynamic mathematical model to describe the performance of jet pipe servo valve under a random vibration environment. Using this model, the reliability and reliability sensitivity varied with most key parameters are extended and reasonable para?meters are recommended on the premise of high reliability and low reliability sensitivity[18]. In the above research, the research on the dynamic per?formance of the pilot stage of the servo valve is still scarce. This defect makes it difficult to es?tablish the dynamic mathematical model of the armature assembly correctly, which is one of the important steps to guide the performance optim?ization of the armature assembly from the theor?etical perspective.

In this regard, the aim of this paper is to es?tablish the dynamic relationship between the jet force, flow field of the pilot stage and the mov?ing flapper of the nozzle flapper servo valve based on the numerical simulation, which is an important part of the dynamic mathematical model for the armature assembly.

1 Armature Assembly Force Analysis

The structure of flapper nozzle servo valve is shown in Fig. 1a, it includes three parts which are torque motor, pilot stage and main spool.The armature assembly will deform under the driving of three external forces which are electro?magnetic force, jet force and feedback force from the feedback rod as shown in Fig. 1b. Compar?ing with the remaining external forces, the calcu?lation result of the jet force usually produces a large error due to its complex structure and high frequency vibration, which also makes it too diffi?cult to measure by the experiment method.Therefore, the method of numerical simulation has become the best way to obtain the dynamic performance of jet force. With this result, the transient dynamic model of the armature as?sembly will be improved.

Fig. 1 Structure of flapper nozzle servo valve

2 Numerical Simulation Model

2.1 Governing equation and solving strategies

The numerical simulation is implemented by the software STAR?CCM 2019. The governing equation is based on the continuity equation and momentum conservation equation which can be expressed as

and

By using the k?e turbulence model which is the transport equation of turbulent flow energy,volume of fluid and the Schnerr?Sauer cavitation model, the main solving equations of the simula?tion program are formed. The fluid is assumed to be incompressible.

2.2 3D simulation model and boundary condition

For reducing the computation time, the 3D simulation model of the servo valve pilot stage is simplified just around the nozzle and flapper as shown in Fig. 2. The main areas of the jet force acting on the flapper are included in this 3D model. The boundary conditions are also plotted in Fig. 2 according to the structure of pilot stage.The inlet and outlet are set as the pressure inlet/outlet, and the value of the pressure outlet is 0 MPa. The liquid used is 10# aviation oil whose gas?liquid two?phase property is listed in Tab.1.

Fig. 2 Structure of numerical simulation model

Tab. 1 Oil property

In order to realize the movement of the flap?per in the flow field, the overlap mesh is em?ployed by the software STAR?CCM 2019, and its region is shown in Fig. 2a, and the parameters of the nozzle centerline cross section are shown in Fig. 2b. It covers the flapper and moves with it.For ensuring the movement of the flapper, the re?gion surround the flapper is refined, and the size of the mesh will be discussed later. The displace?ment function of the flapper is tentatively set as 0.02cos(314.159 3t) whose amplitude will cover the flapper movement range, here t is the physic?al time. Since the moving speed of the flapper is calculated by this equation, the fluid?solid coup?ling method in this paper is the one?phase fluid?solid coupling. The frequency of the flapper movement is 50 Hz, and inlet pressure is set as 6 MPa.

2.3 Numerical simulation model verification

To verify the effectiveness of the numerical simulation model for the flow field of servo valve pilot stage, different settings of the model are tried including the size of the mesh, the length of the time step and the number of the inner itera?tion for every time step. The numerical simula?tion model after verification can seek a balance between the numerical simulation accuracy and the computational cost.

In the verification process of mesh independ?ence, the basic size of overlap mesh regions is se?lected for comparison. The relationship between the mesh of different regions in the fluid field is proportional to implementing the movement of the overset mesh. Therefore, the mesh size of other region will change according to the vari?ation of overlap mesh size.

Four sizes of the overlap mesh are selected for comparison, which is 3.0 mm, 2.5 mm, 2.0 mm and 1.5 mm respectively, and their forces acting on the flapper along the nozzle axial are shown in Fig.3. The curve of 3 mm mesh is totally differ?ent from the other curves, its amplitude is big?ger than those of the other curves and the fluctu?ation is also more intense. The curve of 2.5 mm mesh is basically the same as the remaining two curves except that the force near the amplitude is significantly larger. The remaining two curves have a high degree of coincidence, whose amp?litude and the positions of fluctuation are the same. Thus, the mesh size of 2.0 mm is selected in the following numerical simulation program.

Fig. 3 Mesh size verification

The length of the time step is another factor affecting the accuracy of simulation result. Four types of time steps are simulated, which is 100 μs,50 μs, 10 μs and 5 μs respectively, and the com?parison is still about the force acting on the flap?per as plotted in Fig.4. At the beginning of simu?lation, the force calculated by the mesh size of 100 μs and 50 μs generate a violent oscillation which does not exist in the other two curves. The amplitude of 100 μs time step is bigger than those of others curves, and the curve of 50 μs has a certain lag. Observing the curves of 10 μs and 5 μs, the positions and amplitudes of fluctuation are basically the same. Therefore, the time steps of 100 μs and 50 μs can not meet the accuracy requirements. To save the computing resources,the time step of 10 μs is employed in the follow?ing program.

Fig. 4 Time step verification

The last parameter to be determined is the number of inner iteration step. Four different numbers are tried as 3, 5, 7 and 10, which are plotted in Fig.5. Different from the two paramet?ers mentioned before, different inner iteration steps have little effects on the simulation results.Except for the slightly larger amplitude of the fluctuations when the inner iterations step is 3,the remaining curves are almost indistinguish?able. Therefore, the inner iteration steps of 5 is chosen for the numerical simulation model to re?duce the computation time.

Fig. 5 Inner iterations verification

3 Numerical Simulation Results

3.1 Comparison between the moving and fixed flapper

The previous achievements for the flow field numerical simulation in the pilot stage of servo valve use the flapper fixed in different positions to observe the flow field performance when the flapper moves[2?3]. So, the comparison of the flow field characters between the moving and fixed flapper is first implemented.

The numerical comparison results are plot?ted in Fig. 6. Seven positions of the flapper are selected for comparison where the force acting on the flapper changes violently or the flapper is at the midpoint or vertex, and the comparison res?ults of the force values are shown in Tab. 2. It can be seen that in the area of the force chan?ging rapidly, the difference between the static and transient simulation methods is distinct. The force predicted by the transient simulation is four times larger than that of the static method where the biggest difference occurs. When the force changing is not obvious, the simulation results of the two methods are basically the same, such as the error of the point at 5 ms is only 1%.

Fig. 6 Characteristics comparison of the flow field with moving and fixed flapper

Tab. 2 Armature assembly material properties

The cross section along the center line of the nozzle is selected for the observation for the flow field and cavitation distributions comparison at point ① (1.86 ms) and ② (8.35 ms) as shown in Fig. 6, and all the cross sections used in the fol?lowing content are this cross section. As can be seen, there are certain differences between transi?ent and static simulations. The jet directions pre?dicted by the two methods are significantly dif?ferent when they just leave the flapper as plot?ted, this leads to a difference in predicting the position of the vortex and the force acting on the flapper. The distribution of the cavitation at point ① are similar, the only distinction is the bigger cavitation volume near the flapper simu?lated by the transient method. The cavitation distribution of the two methods are discriminate at point ②, the location of the cavitation pre?dicted by the static simulation is mainly around the flapper, while that of the transient simula?tion is near the nozzle. In the case that the flow field distribution, cavitation distribution, and the force acting on flapper predicted by the static simulation and transient simulation are quite dif?ferent, the transient simulation is obviously closer to the real situation because of the con?tinuity of simulation process.

3.2 Analysis of force acting on moving flapper

In order to establish the relationship bet?ween the position and the force of the flapper during the flapper movement, the force acting on the flapper in a certain period is analyzed.

As the movement trajectory of the flapper and the structure of pilot stage are symmetrical,the force acting on the flapper passing through the same position and the symmetrical position is compared as shown in Fig. 7. The curve of 0–1/4 period is the original curve, 1/4–1/2 period curve presents the curve which is symmetrical to the original curve between 1/4–1/2 period along the axial of t=5 ms, and the curve of 1/2–3/4 is ob?tained by multiplying the original curve between 1/2–3/4 period by –1. It can be seen that the curves of 0–1/4 and 1/2–3/4 period are very sim?ilar while the curve of 1/4–1/2 period is clearly different. It means that the force acting on the flapper in the first half period is the same as that of the second half but the directions are opposite.The force generates an obvious difference when the flapper passes through the same position but different directions. Therefore, the complete force analysis of the flapper can be obtained by just observing the first half of one period.

Fig. 7 Force comparison of flapper at different positions in one period

Through numerical simulation, the force act?ing on the flapper and the distribution of the flow field in the pilot stage during the first half period are obtained as plotted in Fig. 8. Seven points are marked where the force changes dra?matically or the flapper moves to the furthest po?sition. During the first half period, the flapper moves to one side and returns back to the mid?point, the shape of the force curve is basically si?nusoidal with some severe fluctuations. The point① is the position before the force beginning to shock violently, and point ② and ③ is the posi?tion where the force changes dramatically. Dur?ing this process, the distribution of pilot stage flow field changes obviously. Four vortices are generated in the flow field when the flapper just leaves the equilibrium position, two on each side with the basically same size as marked in Fig. 8.As the flapper continues to move, the vortices on the same side begin to deform, which destroys the symmetrical distribution. The jet becomes a direct shot and the vortex on the nether side re?tracts to the lower right corner of the flow field which is away from the edge of the flapper at point ③. These phenomena have caused a huge rise of the force acting on the flapper. Sub?sequently, the flow field of the same side returns to an almost symmetrical distribution when the flapper moves to the farthest position at point⑤, and the force no longer fluctuates. As the flapper moves back, the pilot stage flow field also experiences the process of the two vortexes in one side changing from the basic symmetry to a smaller vortex below at point ⑥, and finally back to the basic symmetry. The force acting on the flapper still rises dramatically as the vortex changes at point ⑥. The large cavitation is the exist with the force fluctuation at point ⑦ as shown, which is different from the previous cavit?ation distribution. Due to the symmetry, the half?period analysis of the pilot stage flow field and the flapper force is sufficient to reflect their all dynamic characteristics.

For building a complete relationship between the jet force and moving flapper, different condi?tions of the servo valve pilot stage are simulated including diverse inlet pressures of the nozzle and the frequencies of moving flapper. The simula?tion results of jet force under different inlet pres?sures are shown in Fig. 9, the frequency of flap?per vibration is 50 Hz. The inlet pressure changes from 1 MPa to 6 MPa which covers the pressure variation range of servo valve pilot stage. From the general trend, the jet force increases with the inlet pressure, and the shape of force curves are sinusoidal. The only difference is the number of the fluctuations, which will almost disappear when the inlet pressure is between 1 MPa and 3 MPa. As the inlet pressure reaches 4 MPa, the fluctuation becomes violent especially when the vortex changes its location as mentioned before.The jet forces acting on the flapper with differ?ent frequencies of the flapper vibration are plot?ted in Fig. 10, and the inlet pressure is 6 MPa.Similar to the situation of different inlet pres?sures, the force curves are basically the same in the low vibration frequency. When the frequency reaches 500 Hz, the whole curve is full of fluctu?ations and the sinusoidal shape almost disap?pears.

Fig. 8 Variation of pilot stage in single period

Fig. 9 Jet force of the flapper with different inlet pressures

In summary, the relation between the force acting on the flapper and the flow field of pilot stage under different inlet pressures and vibra?tion frequencies is analyzed and established. This relationship will be an important part in the fol?lowing research on the mathematical modelling of the armature assembly motion equation.

Fig. 10 Jet force of the flapper with different vibration frequencies

4 Experiment Verification

The visualization and stress experiment are implemented to verify the numerical simulation results. In order to facilitate the measurement of the jet force, only one side of the inlet nozzle is open, and so is the numerical simulation.

The experimental equipment is shown in Fig. 11. The upper and bottom covers of the pi?lot stage assembly are replaced by glass plates as shown in Fig. 11b, and the halogen lamp is placed under the bottom cover which make it available to observe the cavitation distribution of the pilot stage. The experimental schematic dia?gram is plotted in Fig. 11c. The cavitation com?parison of experiment and numerical simulation is shown in Fig. 12 including four pressures 6 MPa, 5 MPa, 3 MPa and 1 MPa as plotted in Figs. 12a, 12b, 12c and 12d respectively. Due to the symmetry of the flow field structure, a quarter of the cross section is selected for com?parison. When the inlet pressure is 6 MPa, the cavitation is mainly generated at three areas as plotted in Fig. 12a, it is the same as that pre?dicted by the numerical simulation. As the inlet pressure decreases, the volume of cavitation re?duces. The cavitation located near the flapper and in the gap of the nozzle and flapper disap?peared when the inlet pressure is 3 MPa, and the cavitation near the corner will also vanish when the inlet pressure decreases to 1 MPa. This pro?cess of transformation is basically confirmed by the numerical simulation. The only distinction is that the cavitation near the flapper and gap pre?dicted by the numerical simulation is still exist?ing rarely with the inlet pressure 3 MPa and 1 MPa.

Fig. 11 Experiment equipment

Fig. 12 Cavitation comparison of the experiment and simula?tion

Due to the small size of the flapper and tightly closed space of the pilot stage, it is diffi?cult to directly measure the jet force acting on the flapper. Hence, a semi?empirical formula is utilized based on the jet flow rate measured by the experiment. The formula is[19]

With the semi?empirical formula and numer?ical simulation, the jet force comparison is ob?tained as shown in Fig. 13. As can be seen, the force predicted by the numerical simulation is lower than that of the experiment, the average error is about 37%. The main reason for this er?ror is the simplification of numerical simulation model, which reduces the bearing area of the flapper. Although the error exists between two results, the same trend can still verify the effect?iveness of the simulation method for the jet force prediction.

Fig. 13 Jet force comparison of the semi?empirical formula and simulation results

5 Conclusions

In this paper, a numerical simulation model based on the flow?solid interaction is applied for investigating the variation of the pilot stage flow field in the nozzle?flapper servo valve. For ensur?ing the effectiveness of the numerical simulation,different mesh sizes, time steps and inner itera?tions step are employed, and the results show that the mesh size of 2 mm, time step of 10 μs and 5 inner iterations step can balance the nu?merical simulation accuracy and the computa?tional cost.

The jet force and distribution of pilot stage flow field are compared between the simulation of moving and fixed flapper, respectively. The vis?ible distinction is revealed between the results,and the distributions of the vortex are obviously different either.

The jet force and flow field variation during the movement of flapper in one period are ana?lyzed, the relationship between the jet force, in?let pressure and flapper vibration frequency is es?tablished which indicates that the number of fluctuations will increase as the pressure and fre?quency increase.

The cavitation distribution and jet flow rate of the pilot stage are measured by experimental methods, and the jet force is also obtained with the basis on the jet flow rate. By comparing with the experiment data, the effectiveness of numeric?al simulation in predicting the variation of the jet force and cavitation is verified, which will offer a base for the follow?up research of the mathemat?ical modelling of armature assembly dynamic re?sponse.